Don't ever let the books convince you you need a ton of stuff to take care of an infant — you don't. Cribs, bottle-warmers, wipe-warmers ... much of what you see in catalogues is wholly unnecessary. Some items like changing tables, swings, bottles, strollers and more can be useful later, or in certain limited circumstances, but not usually for a newborn.
Our first son was born in 1998, his brother in 2002. This page is a collection of products we loved during the first couple years of each child's life:
A nursing pillow. Extremely useful, especially for moms who want to spend any time on the computer with a newborn. We used an off-brand knockoff from a discount store, but Boppy is the best-known brand.
A sling or other baby carrier. I actually found that our slings (Over the Shoulder Baby Holder) hurt my back and shoulders, and most women don't have a stay-at-home partner to do the babywearing duties — but the sling saved our lives, because we had a high-needs baby, and he would not sleep unless he was worn. (We also had a Baby Bjorn, but it was rarely used. Until he could sit up unassisted, Boy One preferred the sling.) If we hadn't lost our third baby, I'd have bought a Maya Wrap.
A bed rail. Ours was a beautiful hinged wooden rail, by Evenflo (but since discontinued), which matched our bed; we found it at a garage sale. Any sturdy bed rail with slats spaced less than 2.75" apart will work. With a bed rail, we could put the baby on the outside of the bed — away from his dad, who worried initially about rolling over on him — and outside the quilt (under his own blanket), so we could snuggle without smothering him. We also took it along while traveling. (If you or your partner is uncomfortable with co-sleeping, check out the Arm's Reach co-sleeper, a kind of open-sided bassinet which attaches to the side of your bed. People who've used them generally love them.)
A diaper pail. What you'll like best will probably depend on whether you use cloth, disposables, or both. (If you use cloth, please research the safety issues of soaking diapers — several babies used to die each year from climbing into diaper pails.)
A few clothes in each size — stock up at tag sales and consignment shops before the baby's born! We found these clothes will last up to a week, while traveling or between laundry days:
An infant car seat. (We used the Evenflo On My Way, which was discontinued shortly after Boy Two was born.) While a portable car seat can be useful in a few places like restaurants, please note that car seats are really designed to stay in cars; babies have died falling from them when they're used in places like shopping carts.
Receiving blankets and cloth diapers (flats and prefolds) of various sorts. We used them as changing pads, impromptu mattress covers (while traveling), and cleanup cloths. There are three kinds of thin cloth diapers available at the average Toys 'R' Us; none of them is worth a nickel as a diaper, but they all have different alternate uses! Get some of each.
A diaper bag. We were religious about our first (a custom-made portable changing pad with pockets for equipment), but it's now impossible to find. Experiment till you find something you like.
Onesies. For newborns in the summer, they're fabulous. I understand they're excellent as an underlayer for babies born at other times, too.
Board books by Sandra Boynton. If you haven't seen any, go to your nearest bookstore, and you'll fall in love, I promise. Our sons' first book was Oh My Oh My Oh Dinosaurs! — and at school age, they're still fans.
Lansinoh. Moms who have any nipple soreness will find this stuff a godsend. Even in 1998 it was ten bucks a tube, but nothing on earth works as well, and it's completely safe for the baby!
Nursing tops (and, if you wear them, dresses). I simply stopped wearing bras a few weeks after giving birth, and switched to wearing only loose tops I could lift to nurse. But when you have to dress up to go somewhere, clothes designed for nursing are great. Motherwear has high catalogue prices but runs a factory outlet in Northampton, MA; they also now sell overstock online, via eBay.
For moms who work outside the home, or moms with frequent nursers who need a break: a good breast pump, a few bottles, and accessories. I highly recommend Avent's Isis hand pump, their microwave sterilizer, and their bottles. (We never froze breastmilk, so I can't recommend storage bags.) I also owned Medela's heavy-duty electric Pump in Style, which was very good, but an expensive purchase if used only for occasional outings.
Again, most of the stuff you'll see in stores is superfluous. Here's what we actually used during our children's first year:
diapers: After our first month with the first child, we switched to store-brand disposables for day use and Huggies Overnights for nighttime; perhaps if better cloth diapers had been available, we'd have chosen differently.
homemade baby wipes: We made our own using baby oil, baby bath, paper towels and a Rubbermaid container.
travel wipes for the diaper bag: We preferred not to expose our babies to the irritating materials in commercial wipes at home, but found that homemade ones were difficult to transport.
diaper-rash ointment: Desitin, A&D, and their store-brand equivalents were, in our experience, roughly equivalent.
cotton balls for the newborn period: Wipes, even homemade ones, are too harsh for newborn diaper changes!
baby bath and baby shampoo: I do wish I'd known at the time about the carcinogens in some baby shampoo, but unscented and "natural" varieties are quite useful.
baby washcloth and towel, baby hairbrush: These aren't necessary in the least, but we actually liked ours!
fingernail clippers: These are for use after the first month or two, when nails are still soft enough to peel.
infant Tylenol: This is an exceedingly dangerous medicine, but a gift from heaven nonetheless. Do not store it within reach of small children — a lethal dose is only twice an effective one — and never, ever confuse the dosage of the infant drops with the children's liquid version. But for fevers and pain, it works miracles.
simethicone (anti-gas medication): The second of the medicines from heaven. Especially valuable when you're dealing with colic. And, unlike Tylenol, extremely difficult to overdose on.
thermometers: Don't get glass/mercury thermometers — they're dangerous, especially for rectal use. We used a digital underarm thermometer when our firstborn was small, but when he was two his grandparents gave us an expensive instant-read ear thermometer ... we thought these things were terrific, and suggested that our friends all mortgage their houses to get one. Turns out their accuracy isn't that great, but I've still found them considerably easier to use, for a ballpark temperature, than fumbling with other types of thermometers.
nasal aspirators (pointy bulbs work better on small babies, two-piece bulbs on toddlers): You won't understand these until you have a baby with a first cold who can't breathe, and you realize the baby can't blow the congestion out alone. If it had been available when our boys were small, I'd have gotten a Nosefrida -- many parents rave about it!
teething tablets: I'm not aware of any evidence that these actually kill teething pain, but they're sweet and make a good placebo. (However, I can no longer recommend anything made by Hyland, which has had severe problems with quality control.)
charcoal, and syrup of ipecac: For the first-aid kit, in case of accidental poisoning or medication overdose. Have the directions, and the number of Poison Control, where you can get to them fast.
Now you know most of what there is to know about buying for a small baby!